Digital Commons Network^™

Imperfect Immunity And The Stability Of A Modified Kermack-Mckendrick Model, Kaylee Sims

Honors Theses

The classic Kermack-McKendrick model of mathematical epidemiology suggests that a population is only in equilibrium when there is no disease present. In the modern era, we have several cyclic infectious diseases that show no signs of eradication, despite global health measures. In this thesis, we introduce a coefficient of waning immunity in order to produce a modified Kermack-McKendrick model and analyze whether the model yields system stability with a certain amount of infection present. Ultimately, the model is incongruent with real-world case data, with its most glaring failure being exponential dampening of the height of each disease case peak due …

An Application Of The Pagerank Algorithm To Ncaa Football Team Rankings, Morgan Majors

Honors Theses

We investigate the use of Google’s PageRank algorithm to rank sports teams. The PageRank algorithm is used in web searches to return a list of the websites that are of most interest to the user. The structure of the NCAA FBS football schedule is used to construct a network with a similar structure to the world wide web. Parallels are drawn between pages that are linked in the world wide web with the results of a contest between two sports teams. The teams under consideration here are the members of the 2021 Football Bowl Subdivision. We achieve a total ordering …

Mathematics And Special Education Co-Teaching In The Middle School: How Teachers Make Sense Of Their Partnership, Bethany Lavalley

Electronic Theses and Dissertations

Co-teaching is the practice of general educators and special educators sharing instruction in a general education setting to deliberately meet the needs of students with and without disabilities. Co-teacher research tends to focus on the processes of co-teaching, and little is known about how teachers go about creating a system of interconnected professional expertise that flexibly meets the diverse learning needs of students. This comparative case study examines the interpersonal and professional relationships of two co-teaching teams who were supported by their respective administration, who shared common planning time, co-instructed together in the mathematics classroom, and were engaged in a …

The Efficacy Of The Covid-19 Vaccine In Mississippi, Ilyse Miriam Levy

Honors Theses

The Efficacy of The COVID-19 Vaccine in Mississippi

(Under the direction of Dr. Xin Dang)

By tracking and analyzing fifty-three weeks of COVID-19 data, this thesis analyzes the efficacy of the COVID-19 vaccine within the State of Mississippi. Over the course of these fifty-three weeks, I have also been able to calculate the confidence intervals for vaccination efficacy and the risk reduction due to vaccination by using data regarding the correlations between deaths and vaccination status, provided to me by the Mississippi Office of Epidemiology. My analysis demonstrates that the COVID-19 vaccine is effective not only in Mississippi but also …

Effective Response To Intervention In Middle School, Angela Mechelle Ellison

Electronic Theses and Dissertations

This applied mixed methods program evaluation sought to increase student proficiency in mathematics at a rural middle school in central Mississippi. The program focused on improving student achievement through effective professional development. Quantitative and qualitative data was used to gage the program’s effectiveness. Research supporting an effective Response to Intervention Model, professional learning communities, and teacher development was cited and used to construct the program’s implementation framework.

Two Way Street: An Applied Research Study On The Effects Of Increased Parent And Community Involvement Activities On Student Academic Growth In Mathematics At South Lee Middle School, Jason Clifton Arledge

Electronic Theses and Dissertations

The purpose of this study was two-fold. The first overarching goal was to increase student academic growth on the Mississippi Academic Assessment Program mathematics assessment to at least 75%. This was attempted through implementation of grade-level Remind services and the Red Raider Family program. The second overarching goal was to create a cycle of continuous improvement through feedback from key stakeholders in the form of surveys, interviews, focus groups, document analysis, and descriptive statistics. South Lee Middle School evaluated each of these initiatives and utilized resources to adjust these programs for use in the 2018-2019 school year.

Cramer Type Moderate Deviations For Random Fields And Mutual Information Estimation For Mixed-Pair Random Variables, Aleksandr Beknazaryan

Electronic Theses and Dissertations

In this dissertation we first study Cramer type moderate deviation for partial sums of random fields by applying the conjugate method. In 1938 Cramer published his results on large deviations of sums of i.i.d. random variables after which a lot of research has been done on establishing Cramer type moderate and large deviation theorems for different types of random variables and for various statistics. In particular results have been obtained for independent non-identically distributed random variables for the sum of independent random to estimate the mutual information between two random variables. The estimates enjoy a central limit theorem under some …

A First-Year Teacher’S Implementation Of Short-Cycle Formative Assessment Through The Use Of A Classroom Response System And Flexible Grouping, Adrienne Irving Dumas

Electronic Theses and Dissertations

As teachers we are tasked with ensuring that our students are equipped with the skills necessary to not only perform with proficiency on local state and national assessments but also to provide our students with opportunities to develop confidence and competence as learners of mathematics through meaningful challenging and worthwhile activities. As such many teachers have turned to technology and cooperative groups as staples in the classroom. The purpose of this study was to understand how one first-year teacher implemented what she was taught in her undergraduate coursework in teaching two specific units of instruction in two sections of high …

Beta Invariant And Variations Of Chain Theorems For Matroids, Sooyeon Lee

Electronic Theses and Dissertations

The beta invariant of a matroid was introduced by Crapo in 1967. We first find the lower bound of the beta invariant of 3-connected matroids with rank r and the matroids which attain the lower bound. Second we characterize the matroids with beta invariant 5 and 6. For binary matroids we characterize matroids with beta invariant 7. These results extend earlier work of Oxley. Lastly we partially answer an open question of chromatic uniqueness of wheels and prove a splitting formula for the beta invariant of generalized parallel connection of two matroids. Tutte's Wheel-and-Whirl theorem and Seymour's Splitter theorem give …

Feedback In The Flipped High School Stem Classroom, Trisha Michele Gilbreath

Electronic Theses and Dissertations

This study examined how much feedback students received in the flipped high school science, technology, engineering and math (STEM) classroom. The flipped classroom is a pedagogical technique where students watch video instruction at home and complete collaborative activities in class. This technique has gained popularity in recent years, especially in STEM classrooms. The literature on the flipped classroom is inconclusive, with studies mainly conducted in higher education. Student and instructor perceptions were often studied, and those perceptions are generally positive about the flipped classroom, though there are concerns to consider. Student performance shows that the flipped classroom is at least …

An Examination Of The Relationship Among The Intentions, Features, Affordances, And Outcomes Of Saturday Academy For Math Professional Development For Mathematics Teachers, Brian Buckhalter

Electronic Theses and Dissertations

Using a design framework to connect the features of SA4M to the affordances reported, participants of SA4M deepened their content knowledge on both conceptual and skill specific levels, and expressed intentions to incorporate many of the tasks from SA4M into their practices. There are implications for those tasked with creating and evaluating professional development for teachers.

Mathematical Tasks Without Words And Word Problems: Perceptions Of Reluctant Problem Solvers, Sydney Margaret Holbert

Electronic Theses and Dissertations

This qualitative research study used a multiple, holistic case study approach (Yin, 2009) to explore the perceptions of reluctant problem solvers related to mathematical tasks without words and word problems. Participants were given a choice of working a mathematical task without words or a word problem during four problem-solving sessions. Data were gathered from problem-solving sessions, in the form of session transcripts, written reflections, and interviews to determine how the reluctant problem solvers perceived the problems presented in each session. Participants' views of the problems before and after working were recorded and thick descriptions of the sessions including quotes from …

A Comparison Of Online And Face-To-Face Discussions In An Elementary Mathematics Methods Course, Julie Stephens James

Electronic Theses and Dissertations

The purpose of this qualitative study was to determine if there is a difference between online and face-to-face discussions in terms of quality of responses. The researcher analyzed discussions among teacher candidates enrolled in a web-enhanced undergraduate elementary mathematics methods course. Data was collected through surveys, audio-recordings of face-to-face discussions and asynchronous discussion board transcripts. Transcripts from online and face-to-face discussions were analyzed for evidence of critical thinking using the practical inquiry model (Garrison, Anderson & Archer, 2001). The researcher found that discussions that utilized the asynchronous discussion board elicited more critical thinking from participants than face-to-face discussions. Also, the …

Secondary Mathematics' Teachers Perceptions Of Their Integration Of Instructional Technologies, Jessica Taylor Ivy

Electronic Theses and Dissertations

This qualitative research study explored the beliefs and practices regarding integrations of instructional technologies by seven secondary mathematics teachers. The researcher conducted an initial interview, a classroom observation, and a follow-up interview with each participant. Participants also submitted sample lessons and completed a TPACK Development Model Self-Report Survey. The interviews and observations were analyzed using deductive analysis, using the Technological Pedagogical Content Knowledge (TPACK) Development Model to assess technology-related practices. Through responses to the TPACK Development Model Self-Report Survey, the participants revealed their perceptions of their practices and beliefs regarding technology integration. These perceptions were compared to the researcher's analysis …

An Examination Of Secondary Mathematics Teachers' Tpack Development Through Participation In A Technology-Based Lesson Study, Julie Whitten Riales

Electronic Theses and Dissertations

This qualitative research study used a layered case study (Patton, 2002) to examine the technological, pedagogical, and content knowledge (TPACK) of a group of inservice secondary mathematics teachers as they participated in a technology-based lesson study. Using the TPACK Development Model (Niess, 2009) as a lens, this dissertation examines interactions of the group members during lesson study meetings as well as individual case studies of four of the six participants. Data were gathered from initial surveys, initial and post-interviews, initial and post-classroom observations, writing prompts, and transcriptions of lesson study group meetings. Data were analyzed to determine the TPACK development …